simulation of electro-thermal transients in ... · the electro-thermal model for the lhc main...
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Simulation of Electro-Thermal Transients
in Superconducting Accelerator Magnets
with COMSOL Multiphysics ®
L. Bortot1, M. Maciejewski1,2, M. Prioli1, A.M. Navarro1, S. Schöps3,
I. Cortes Garcia3, A. B. Auchmann1, and A.P. Verweij1
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1) 2) 3)
lorenzo.borot @ cern.ch
Special thanks to Dr. Friedel and COMSOL Switzerland
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LHC – The Large Hadron Collider
The Mont Blanc
Geneva airport
15 m
30 ton
8.33 T
1.9 K
12 kA
X 1500
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Electrodynamics
Fluid dynamics
ThermalMechanics
…
Multi-Physics
Multi-Rate
Multi-Scale
1e-61e-31
Liquid He @1.9 K
1000 A/mm2
The 8.33 Tesla, Twin-Aperture, LHC Dipole Magnet
[m]
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Propagation!
The stored energy in the
magnet is released as
Ohmic losses:
7 MJ
20 tons truck @ 95 km/h
Superconductivity is related to
the material’s Critical Surface
( J [A/mm2], B [T], T [K] ).
If the working point moves
beyond the surface, it triggers
a local transition from the
superconducting to the normal
conducing state.
A resistive zone that produces
enough heat to grow is called
Quench.
Why Do We Need Simulations
Simulations support the
prevention of disruptions!
Quenches
cannot be
avoided.
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Modelling: Challenges
Magnetic formulation
Complex geometry for
both, cable and strand
Eddy-currents
Magnetization
Hysteresis
Material properties
Very small heat
capacity @ 1.9 K
Variation of several
orders of magnitude
within 100 K
Non-linearity
Discontinuities
Nb-Ti Superfluid Helium
four different conduction
regimes within four Kelvin
Helium phase transition
Not modelled yet
(under investigation)
Quench transition
Discontinuity
Numerical instability
Need for smoothing
functions (Sigmoids)
~um
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User’s Input
Magnet features
model
Solver
Post-processing
C-functions
Material Properties
API
Numerical
Engine
Modelling - Construction
• 320 domains (cable cross sections)
• Domain-dependent equations
• GUI workflow risky, slow, error-prone
• Automation as solution
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Modelling – Eddy-Currents
CERNcourier.com
How to discretize a superconducting cable?
~100 um
Wilson / Verweij equivalent magnetization
• Formulation
• Constitutive law
• Ampere-Maxwell Law
If the eddy-currents paths are known a priori,
The equivalent magnetization effect can be directly
related to the change of magnetic flux density
Faraday-Lenz + Ampere-Maxwell
μ0μr Meddy = τeq𝜕B
𝜕t
B = μ0μr H + Meddy
σ𝜕A
𝜕t𝛻 × M eddy
Eddy-currents’ paths don’t have
to be resolved anymore!
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Modelling – Thermal Balance
• Coil insulation
An accurate insulation modelling is critical
for the simulation of a quench propagation
Homogenized insulation
Combination of 1-D General layers
and 2-D explicit domains
Manual, error-prone insulation assignment
Multi-layer insulation, up to 7 layers
Multi-material insulation
Layer orientation (upside-downside)
Interfaces among insulation layers
Inter-layer
insulation foil
Wedge
insulationTurn insulation
Insulation foils
How to Mesh?
Heat
mapping?
Automatic
insulation
handling?
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Modelling - Details
WedgeCoil
Air Gap
Definitions:
Wide use of external C-functions,
performant and flexible enough for
the non-linear material properties
Mesh:
Combination of structured and
unstructured elements, to
minimize the number of nodes
Time dependent study:
Two concatenated studies, linear
ramp-up and exponential decay of
the magnet’s current
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Results – Magnetic field
Linear current ramp-up: of 100 A/s, up to 11.85 kA
Magnetic flux density [ T ] Eddy-currents equivalent magnetization [ A/m ]
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Results – Heat Balance
Eddy-currents losses [ W/m3 ] Ohmic losses [ W/m3 ] Temperature [ K ]
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Conclusions and Outlook
The complexity of the model construction is
handled via a dedicated Java workflow, based
on the COMSOL API.
An equivalent magnetization model accounts
for the eddy-currents in the magnet’s coil.
Highly non-linear material properties are
managed via external C-functions.
Structured-unstructured mesh coupling allows
to drastically reduce the number of nodes.
The electro-thermal model for the LHC Main
Dipole has been developed, and the related
time domain transient has been investigated.
Coil longitudinal development
Te
mp
era
ture
1-D: Quench initiation and propagation,
both, longitudinally and from turn to turn
3-D: Electro-thermal 2-D: New magnet designs
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Annexess
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Results – Magnetic field
• nominal current • Linear ramp-up of 100 A/s
• 8 kA
Magnetic flux density [ T ] Eddy-currents equivalent magnetization [ A/m ]
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Results – Heat Balance
• Three orders of magnitude
higher than the eddy-currents
losses
Eddy-currents losses [ W/m3 ] Ohmic losses [ W/m3 ] Temperature [ K ]
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Modelling – Thermal Balance
Insulation foil
Inter-layer
insulation foil
Wedge
insulation
Turn insulation
Coil insulation An accurate insulation modelling is critical
for the simulation of a quench propagation
Homogenized insulation
Combination of 1-D General layers
and 2-D explicit domains
Manual, error prone assignment to boundaries
Multi-layer insulation, up to 7 layers
Multi-material
Layer orientation (upside-downside)
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Physics of Superfluid Helium
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Some suggestions:
Slide 1: Maybe add STEAM logoSlide 2: add (or replace the pictures of the detectors) a 3D pictures of a 15 m long dipole, 30 ton, 8 T, 1.9 K, 12 kASlide 3: note that this is 2-D, usually sufficient.Slide 7: a fire is maybe a bit too much…
Maybe spent a few lines on heat transfer to helium (or otherwise put it in the outlook)The names (wedge, outer, interlayer, halfturn) are not very clear
Slide 9, 10, 11: movies are nicer! No Time
Add a slide on difficulties in modelling (SC-n transition, phase transitions helium, very thin insulation layer, very low heat capacity, complicated cable/strand cross section, various dynamic effects such as coupling current and magnetization, hysteresis etc, initial quench propagation is 3D)
Take the occasion to also present the problems in modelling, not only show the good results…
Cheers,Arjan